The function h(t) = –16t^2 + 16t + 32 models the height of a ball t seconds after it was thrown into the air. how long does it take for the ball to hit the ground?

When the ball hits the ground, h will be 0 so set up the equation
-16t^2+16t+32=0
divide all by -16 to simply the equation
t^2-t-2=0
(t-2)(t+1)=0
t=2 t=-1
you can’t have -1 second
so the answer is it takes 2 seconds for the ball to hit the ground